Question

Что такое дивергенция?

Answer 1

Дивергенция — это линейный дифференциальный оператор на векторном поле, характеризующий поток данного поля через поверхность достаточно малой в условиях конкретной задачи окрестности каждой внутренней точки области определения поля.

Answer 2

Оно имеет два значения: 1) Дивергенция (от лат. divergere — обнаруживать расхождение) — дифференциальный оператор, отображающий векторное поле на скалярное (то есть операция дифференцирования, в результате применения которой к векторному полю получается скалярное поле), который определяет (для каждой точки), «насколько расходится входящее и исходящее из малой окрестности данной точки поле» (точнее — насколько расходятся входящий и исходящий поток). 
2) Дивергенция (от средневекового лат. divergo — отклоняюсь) (в биологии) — расхождение признаков и свойств у первоначально близких групп организмов в ходе эволюции, результат обитания в разных условиях и неодинаково направленного естественного или искусственного отбора 

Answer 3

What is Divergence?

Divergence is a term that is used in various fields, including mathematics, physics, finance, and biology. The specific meaning of divergence can vary depending on the context in which it is used. Let's explore a few different interpretations of divergence:

1. Mathematics: In mathematics, divergence refers to a property of vector fields. It measures the tendency of vector field lines to either converge or diverge at a given point. Mathematically, the divergence of a vector field is calculated using the divergence operator, which is denoted by the symbol ∇ · F, where ∇ represents the gradient operator and F represents the vector field. The divergence of a vector field can be positive, negative, or zero, indicating whether the field lines are spreading out, converging, or neither at a particular point.

2. Physics: In physics, divergence is often used in the context of fluid flow. It represents the rate at which fluid is either flowing out of or flowing into a given region. The divergence of a fluid flow field is calculated using the same mathematical concept as in mathematics, where the vector field represents the velocity of the fluid at each point. Positive divergence indicates fluid flowing out of a region, negative divergence indicates fluid flowing into a region, and zero divergence indicates no net flow.

3. Finance: In finance, divergence is commonly used in technical analysis to analyze price movements in financial markets. It refers to a situation where the price of an asset and an indicator, such as a moving average or an oscillator, move in opposite directions. Divergence is often seen as a potential signal of a trend reversal or a change in market momentum.

4. Biology: In biology, divergence is used to describe the evolutionary process by which species gradually accumulate differences over time, leading to the formation of new species. It occurs when populations of a common ancestor become isolated from each other and experience different selective pressures, leading to the development of distinct traits and characteristics.

It's important to note that the specific definition and interpretation of divergence can vary depending on the field in which it is used. The examples provided above are just a few common applications of the concept.